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Dataplot Solution to the Mathematics Problem
Problem Setup An analyst wishes to examine the function x*exp(-x) + sin(x**2) over the interval 0 to 3. Plot the function over the interval. Determine any roots in the interval. Determine its definite integral over the interval.
Dataplot Program This is demonstrated with the following Dataplot program
    LET FUNCTION F = X*EXP(-X) + SIN(X**2)
    TITLE X*EXP(-X) + SIN(X**2)
    PLOT F FOR X = 0 0.1 3
    LET R = ROOTS F WRT X FOR X = 0 TO 3
    LET INT = INTEGRAL F WRT X FOR X = 0 TO 3
Dataplot Output generated the following output

Plot of function 


  
       ********************************************
       **  LET R = ROOTS F WRT X FOR X = 0 TO 3  **
       ********************************************
  
  
 ROOTS OF AN EQUATION
       FUNCTION--(X*EXP(-X)+SIN(X**2))
       ROOT VARIABLE                     = X
       SPECIFIED LOWER LIMIT OF INTERVAL =         0.0000000000
       SPECIFIED UPPER LIMIT OF INTERVAL =         3.0000000000
  
       NUMBER OF ROOTS FOUND IN INTERVAL =        3
  
 ROOT     1 =   0.0000000E+00
 ROOT     2 =   0.1853708E+01
 ROOT     3 =   0.2464136E+01
  
  
 THE NUMBER OF VALUES GENERATED FOR THE VARIABLE R        =        3
  
 THE FIRST          COMPUTED VALUE OF R        =   0.0000000E+00 (ROW     1)
 THE LAST (    3TH) COMPUTED VALUE OF R        =   0.2464136E+01 (ROW     3)
  
 THE CURRENT COLUMN FOR THE VARIABLE R         =        1
 THE CURRENT LENGTH OF  THE VARIABLE R         =        3
  
  
 THE COMPUTED VALUE OF THE CONSTANT   NROOTS   =   0.3000000E+01
  
  
       *************************************************
       **  LET INT = INTEGRAL F WRT X FOR X = 0 TO 3  **
       *************************************************
  
  
 INTEGRAL EVALUATION
       FUNCTION--(X*EXP(-X) + SIN(X**2))
       SPECIFIED LOWER LIMIT OF INTEGRAL  =         0.0000000000
       SPECIFIED UPPER LIMIT OF INTEGRAL  =         3.0000000000
       NUMBER OF VARIABLES OF INTEGRATION =        1
  
 NUMBER OF    *       VALUE OF
 PARTITIONS   *       INTEGRAL
 -------------*--------------------
  
        1     *   0.1574414E+01
        2     *   0.1574414E+01
  
 INTEGRAL VALUE        =   0.1574414E+01
  
  
 THE COMPUTED VALUE OF THE CONSTANT   INT      =   0.1574414E+01

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Date created: 06/05/2001
Last updated: 09/28/2016
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